Answer:
symmetry about the y-axis is shown
Step-by-step explanation:
Points on the right of the line of symmetry (x=0, the y-axis) are the same distance from that line as the corresponding points on the left. (That is what makes it a line of symmetry.)
There is no point of rotation that will map one figure to the other after rotation, hence no point or rotational symmetry.
Answer:there are 16 goats and 22 chickens.
Step-by-step explanation:
Let x represent the number of goats in the field.
Let y represent the number if chicken in the field.
After a quick count, you determine there are 38 heads and 108 feet in the field. A goat has one head. A chicken also has one head. It means that
x + y = 38
A goat has four legs. A chicken has 2 legs. It means that
4x + 2y = 108 - - - - - - - - - - - 1
Substituting x = 38 - y into equation 1, it becomes
4(38 - y) + 2y = 108
152 - 4y + 2y = 108
- 4y + 2y = 108 - 152
- 2y = - 44
y = - 44/ - 2
y = 22
x = 38 - y = 38 - 22
x = 16
Answer:
14,850
Step-by-step explanation:
You need the sum of
3 + 6 + 9 + 12 + ... + 294 + 297
Factor out a 3 from the sum
3 + 6 + 9 + 12 + ... + 294 + 297 = 3(1 + 2 + 3 + 4 + ... + 98 + 99)
You need to add all integers from 1 to 99 and multiply by 3.
The sum of all consecutive integers from 1 to n is:
[n(n + 1)]/2
The sum of all consecutive integers from 1 to 99 is
[99(99 + 1)]/2
The sum you need is 3 * [99(99 + 1)]/2
3 + 6 + 9 + 12 + ... + 294 + 297 =
= 3 * [99(99 + 1)]/2
= 3 * [99(100)]/2
= 3 * 9900/2
= 14,850
Answer:
1. x= -1/3
2. y= -4, x= 2
3. y=-2, x=1
Step-by-step explanation:
